The man was arrested under laws designed to crack down on cyber-crime, contained in India's Information Technology Act.
Police say the case is the only one of its kind in the city.
He has been remanded in police custody until 24 June.
They say the man, Pranab Mitra, is believed to have created several email addresses to help trap his so-called lover in Abu Dhabi.
The chief of Bombay police's crime branch, Satyapal Singh, told the BBC it was a unique case of cyber crime.
LOVE WEB :
Police say the accused, a former executive in a cement company, began his internet-based "romance" exactly a year ago.
The first report registered by Bombay's police's cyber crime cell says Mr Mitra and an Abu Dhabi-based construction advisor, Vinay Ninawe, met on the net and began exchanging emails in which they expressed their love for each other.
Mr Mitra, who allegedly posed as "Rita Basu", then invited Mr Ninawe over to Bombay so they could meet.
But when Mr Mitra failed to show up at the appointed time and place Mr Ninawe returned home.
Mitra is then alleged to have sent an email, accusing him of not turning up in Mumbai and threatening to commit suicide.
Worried over the consequences, Mr Ninawe sent an email to a friend of Mr Mitra called "Ruchira Sengupta".
But police say this person was also Pranab Mitra.
Mr Mitra, posing as Ruchira, allegedly told Mr Ninawe that Rita Basu had already committed suicide in Calcutta.
He added that police there suspected he had driven Rita to take her own life.
Still pretending to be Ruchira he arranged for a lawyer to help Mr Ninawe. But the lawyer was also Mr Mitra.
Police say Mr Mitra later sent emails, posing as Calcutta police and High Court, saying he would soon be summoned to court.
Mr Mitra, while playing the role of the lawyer, gradually kept demanding huge amounts of money from Mr Ninawe
By the time Mr Ninawe became suspicious he had already sent Mr Mitra 9.6 million Rupees, the police said.
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